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<FONT color="green">001</FONT>    package mathtools;<a name="line.1"></a>
<FONT color="green">002</FONT>    <a name="line.2"></a>
<FONT color="green">003</FONT>    import exceptions.MatrixSizeException;<a name="line.3"></a>
<FONT color="green">004</FONT>    import mathtools.Complex;<a name="line.4"></a>
<FONT color="green">005</FONT>    import mathtools.Matrix;<a name="line.5"></a>
<FONT color="green">006</FONT>    <a name="line.6"></a>
<FONT color="green">007</FONT>    /**<a name="line.7"></a>
<FONT color="green">008</FONT>     * Representation of a matrix of elements. Class includes support<a name="line.8"></a>
<FONT color="green">009</FONT>     * for matrix of NxM elements, and elements are Complex elements, <a name="line.9"></a>
<FONT color="green">010</FONT>     * allowing for real and complex number operations.<a name="line.10"></a>
<FONT color="green">011</FONT>     * @author Alex Bush, Richard Inskip, James Hancox<a name="line.11"></a>
<FONT color="green">012</FONT>     */<a name="line.12"></a>
<FONT color="green">013</FONT>    public class Matrix {<a name="line.13"></a>
<FONT color="green">014</FONT>    <a name="line.14"></a>
<FONT color="green">015</FONT>            /** 2D array representation of a matrix */<a name="line.15"></a>
<FONT color="green">016</FONT>            protected Complex[][] m;<a name="line.16"></a>
<FONT color="green">017</FONT>            /** Width of the matrix */<a name="line.17"></a>
<FONT color="green">018</FONT>            protected int width;<a name="line.18"></a>
<FONT color="green">019</FONT>            /** Height of matrix */<a name="line.19"></a>
<FONT color="green">020</FONT>            protected int height;<a name="line.20"></a>
<FONT color="green">021</FONT>    <a name="line.21"></a>
<FONT color="green">022</FONT>            /**<a name="line.22"></a>
<FONT color="green">023</FONT>             * Create an empty matrix of integers of size (NxM) <a name="line.23"></a>
<FONT color="green">024</FONT>             * @param N width of matrix<a name="line.24"></a>
<FONT color="green">025</FONT>             * @param M height of matrix<a name="line.25"></a>
<FONT color="green">026</FONT>             * @param num number for all elements in matrix<a name="line.26"></a>
<FONT color="green">027</FONT>             */<a name="line.27"></a>
<FONT color="green">028</FONT>            public Matrix(int N,int M, double num){<a name="line.28"></a>
<FONT color="green">029</FONT>                    if (N &lt; 1 || M &lt; 1){<a name="line.29"></a>
<FONT color="green">030</FONT>                            throw new MatrixSizeException("Dimensions of matrix must be at least 1x1");<a name="line.30"></a>
<FONT color="green">031</FONT>                    }<a name="line.31"></a>
<FONT color="green">032</FONT>                    m = new Complex[N][M];<a name="line.32"></a>
<FONT color="green">033</FONT>                    for ( int i = 0; i &lt; N; i++ ){<a name="line.33"></a>
<FONT color="green">034</FONT>                            for ( int j = 0; j &lt; M; j++ ){<a name="line.34"></a>
<FONT color="green">035</FONT>                                    m[i][j] = new Complex(num,0);<a name="line.35"></a>
<FONT color="green">036</FONT>                            }<a name="line.36"></a>
<FONT color="green">037</FONT>                    }<a name="line.37"></a>
<FONT color="green">038</FONT>                    width = N;<a name="line.38"></a>
<FONT color="green">039</FONT>                    height = M;<a name="line.39"></a>
<FONT color="green">040</FONT>            }<a name="line.40"></a>
<FONT color="green">041</FONT>    <a name="line.41"></a>
<FONT color="green">042</FONT>            /**<a name="line.42"></a>
<FONT color="green">043</FONT>             * Create an empty matrix with no assigned elements.<a name="line.43"></a>
<FONT color="green">044</FONT>             * Better performance for operations where all elements are guaranteed<a name="line.44"></a>
<FONT color="green">045</FONT>             * to be set (e.g. Tensor product and Multiplication)<a name="line.45"></a>
<FONT color="green">046</FONT>             * @param N width of matrix<a name="line.46"></a>
<FONT color="green">047</FONT>             * @param M height of matrix <a name="line.47"></a>
<FONT color="green">048</FONT>             */<a name="line.48"></a>
<FONT color="green">049</FONT>            private Matrix(int N,int M){<a name="line.49"></a>
<FONT color="green">050</FONT>                    if (N &lt; 1 || M &lt; 1){<a name="line.50"></a>
<FONT color="green">051</FONT>                            throw new MatrixSizeException("Dimensions of matrix must be at least 1x1");<a name="line.51"></a>
<FONT color="green">052</FONT>                    }<a name="line.52"></a>
<FONT color="green">053</FONT>                    m = new Complex[N][M];<a name="line.53"></a>
<FONT color="green">054</FONT>                    width = N;<a name="line.54"></a>
<FONT color="green">055</FONT>                    height = M;<a name="line.55"></a>
<FONT color="green">056</FONT>            }<a name="line.56"></a>
<FONT color="green">057</FONT>    <a name="line.57"></a>
<FONT color="green">058</FONT>            /**<a name="line.58"></a>
<FONT color="green">059</FONT>             * Return the width of this matrix<a name="line.59"></a>
<FONT color="green">060</FONT>             * @return Width of the current matrix<a name="line.60"></a>
<FONT color="green">061</FONT>             */<a name="line.61"></a>
<FONT color="green">062</FONT>            public int getWidth(){<a name="line.62"></a>
<FONT color="green">063</FONT>                    return m.length;<a name="line.63"></a>
<FONT color="green">064</FONT>            }<a name="line.64"></a>
<FONT color="green">065</FONT>    <a name="line.65"></a>
<FONT color="green">066</FONT>            /**<a name="line.66"></a>
<FONT color="green">067</FONT>             * Return the height of this matrix<a name="line.67"></a>
<FONT color="green">068</FONT>             * @return Height of the current matrix<a name="line.68"></a>
<FONT color="green">069</FONT>             */<a name="line.69"></a>
<FONT color="green">070</FONT>            public int getHeight(){<a name="line.70"></a>
<FONT color="green">071</FONT>                    return m[0].length;<a name="line.71"></a>
<FONT color="green">072</FONT>            }<a name="line.72"></a>
<FONT color="green">073</FONT>    <a name="line.73"></a>
<FONT color="green">074</FONT>            /**<a name="line.74"></a>
<FONT color="green">075</FONT>             * Compute the tensor product of two matrices.<a name="line.75"></a>
<FONT color="green">076</FONT>             * @param b Matrix to tensor with<a name="line.76"></a>
<FONT color="green">077</FONT>             * @return c the tensor product this matrix with b<a name="line.77"></a>
<FONT color="green">078</FONT>             */<a name="line.78"></a>
<FONT color="green">079</FONT>            public Matrix tensorProduct(Matrix b){<a name="line.79"></a>
<FONT color="green">080</FONT>                    Matrix c = new Matrix(getWidth()*b.getWidth(),getHeight()*b.getHeight());<a name="line.80"></a>
<FONT color="green">081</FONT>    <a name="line.81"></a>
<FONT color="green">082</FONT>                    for ( int i = 0; i &lt; getWidth(); i++ ){<a name="line.82"></a>
<FONT color="green">083</FONT>                            for ( int j = 0; j &lt; getHeight();j++ ){<a name="line.83"></a>
<FONT color="green">084</FONT>                                    for ( int k = 0; k &lt; b.getWidth(); k++ ){<a name="line.84"></a>
<FONT color="green">085</FONT>                                            for ( int l = 0; l &lt; b.getHeight(); l++){<a name="line.85"></a>
<FONT color="green">086</FONT>                                                    c.setElement(i*b.getWidth()+k,j*b.getHeight()+l,Complex.multiplyComplex(m[i][j],b.getElement(k,l)));<a name="line.86"></a>
<FONT color="green">087</FONT>                                            }<a name="line.87"></a>
<FONT color="green">088</FONT>                                    }<a name="line.88"></a>
<FONT color="green">089</FONT>                            }<a name="line.89"></a>
<FONT color="green">090</FONT>                    }<a name="line.90"></a>
<FONT color="green">091</FONT>                    return c;<a name="line.91"></a>
<FONT color="green">092</FONT>            }<a name="line.92"></a>
<FONT color="green">093</FONT>    <a name="line.93"></a>
<FONT color="green">094</FONT>            /**<a name="line.94"></a>
<FONT color="green">095</FONT>             * Return single element of a matrix.<a name="line.95"></a>
<FONT color="green">096</FONT>             * @param i ith column<a name="line.96"></a>
<FONT color="green">097</FONT>             * @param j jth row<a name="line.97"></a>
<FONT color="green">098</FONT>             * @return Complex element<a name="line.98"></a>
<FONT color="green">099</FONT>             */<a name="line.99"></a>
<FONT color="green">100</FONT>            public Complex getElement(int i, int j){<a name="line.100"></a>
<FONT color="green">101</FONT>                    if (i &gt;= this.getWidth()){<a name="line.101"></a>
<FONT color="green">102</FONT>                            throw new IllegalArgumentException("Argument reference element out of array bounds in matrix width:" + i);<a name="line.102"></a>
<FONT color="green">103</FONT>                    }<a name="line.103"></a>
<FONT color="green">104</FONT>                    else if (j &gt;= this.getHeight()){<a name="line.104"></a>
<FONT color="green">105</FONT>                            throw new IllegalArgumentException("Argument reference element out of array bounds in matrix height:" + j);<a name="line.105"></a>
<FONT color="green">106</FONT>                    }<a name="line.106"></a>
<FONT color="green">107</FONT>                    return m[i][j];<a name="line.107"></a>
<FONT color="green">108</FONT>            }<a name="line.108"></a>
<FONT color="green">109</FONT>    <a name="line.109"></a>
<FONT color="green">110</FONT>            /**<a name="line.110"></a>
<FONT color="green">111</FONT>             * Set an element of this matrix.<a name="line.111"></a>
<FONT color="green">112</FONT>             * @param i ith column<a name="line.112"></a>
<FONT color="green">113</FONT>             * @param j jth row<a name="line.113"></a>
<FONT color="green">114</FONT>             * @param e Complex element to set<a name="line.114"></a>
<FONT color="green">115</FONT>             */<a name="line.115"></a>
<FONT color="green">116</FONT>            public void setElement(int i, int j, Complex e){<a name="line.116"></a>
<FONT color="green">117</FONT>                    if (i &gt;= this.getWidth()){<a name="line.117"></a>
<FONT color="green">118</FONT>                            throw new IllegalArgumentException("Argument reference element out of array bounds in matrix width:" + i);<a name="line.118"></a>
<FONT color="green">119</FONT>                    }<a name="line.119"></a>
<FONT color="green">120</FONT>                    else if (j &gt;= this.getHeight()){<a name="line.120"></a>
<FONT color="green">121</FONT>                            throw new IllegalArgumentException("Argument reference element out of array bounds in matrix height:" + j);<a name="line.121"></a>
<FONT color="green">122</FONT>                    }<a name="line.122"></a>
<FONT color="green">123</FONT>                    m[i][j] = e;<a name="line.123"></a>
<FONT color="green">124</FONT>            }<a name="line.124"></a>
<FONT color="green">125</FONT>    <a name="line.125"></a>
<FONT color="green">126</FONT>            /**<a name="line.126"></a>
<FONT color="green">127</FONT>             * Multiply this matrix by another matrix. Width of this must equal height of b<a name="line.127"></a>
<FONT color="green">128</FONT>             * @param b matrix to multiply this by<a name="line.128"></a>
<FONT color="green">129</FONT>             * @throws illegal argument exception<a name="line.129"></a>
<FONT color="green">130</FONT>             */<a name="line.130"></a>
<FONT color="green">131</FONT>            public Matrix multiplyMatrix(Matrix b){<a name="line.131"></a>
<FONT color="green">132</FONT>                    if ( this.getWidth() != b.getHeight()){<a name="line.132"></a>
<FONT color="green">133</FONT>                            throw new MatrixSizeException("Width of this matrix must be equal to the height of the passed matrix b:\n" +<a name="line.133"></a>
<FONT color="green">134</FONT>                                            "this width: " + this.getWidth() + " b height: " + b.getHeight());<a name="line.134"></a>
<FONT color="green">135</FONT>                    }<a name="line.135"></a>
<FONT color="green">136</FONT>                    Matrix c = new Matrix(b.getWidth(),this.getHeight());<a name="line.136"></a>
<FONT color="green">137</FONT>    <a name="line.137"></a>
<FONT color="green">138</FONT>                    for ( int i=0; i &lt; c.getHeight(); i++){<a name="line.138"></a>
<FONT color="green">139</FONT>                            for ( int j = 0; j &lt; c.getWidth(); j++){<a name="line.139"></a>
<FONT color="green">140</FONT>                                    Complex e = new Complex(0,0);<a name="line.140"></a>
<FONT color="green">141</FONT>                                    for ( int k = 0; k &lt; this.getWidth(); k++){<a name="line.141"></a>
<FONT color="green">142</FONT>                                            e = Complex.addComplex(e, Complex.multiplyComplex(this.getElement(k, i), b.getElement(j, k)));<a name="line.142"></a>
<FONT color="green">143</FONT>                                    }<a name="line.143"></a>
<FONT color="green">144</FONT>                                    c.setElement(j, i, e);<a name="line.144"></a>
<FONT color="green">145</FONT>                            }<a name="line.145"></a>
<FONT color="green">146</FONT>                    }<a name="line.146"></a>
<FONT color="green">147</FONT>                    return c;<a name="line.147"></a>
<FONT color="green">148</FONT>            }<a name="line.148"></a>
<FONT color="green">149</FONT>    <a name="line.149"></a>
<FONT color="green">150</FONT>            /**<a name="line.150"></a>
<FONT color="green">151</FONT>             * A method to multiply a matrix by a constant.<a name="line.151"></a>
<FONT color="green">152</FONT>             * @param constant Constant represents any double to multiply the matrix by<a name="line.152"></a>
<FONT color="green">153</FONT>             * @return Matrix c<a name="line.153"></a>
<FONT color="green">154</FONT>             */<a name="line.154"></a>
<FONT color="green">155</FONT>            public Matrix multiplyMatrix(double constant){<a name="line.155"></a>
<FONT color="green">156</FONT>                    Matrix c = new  Matrix(this.getWidth(),this.getHeight());<a name="line.156"></a>
<FONT color="green">157</FONT>    <a name="line.157"></a>
<FONT color="green">158</FONT>                    for ( int i=0; i &lt; c.getHeight(); i++){<a name="line.158"></a>
<FONT color="green">159</FONT>                            for ( int j = 0; j &lt; c.getWidth(); j++){<a name="line.159"></a>
<FONT color="green">160</FONT>                                    c.setElement(j, i,Complex.multiplyComplex(constant,this.getElement(j, i)));<a name="line.160"></a>
<FONT color="green">161</FONT>                            }<a name="line.161"></a>
<FONT color="green">162</FONT>                    }<a name="line.162"></a>
<FONT color="green">163</FONT>                    return c;<a name="line.163"></a>
<FONT color="green">164</FONT>            }<a name="line.164"></a>
<FONT color="green">165</FONT>    <a name="line.165"></a>
<FONT color="green">166</FONT>            /**<a name="line.166"></a>
<FONT color="green">167</FONT>             * A method to multiply a matrix by a constant complex number.<a name="line.167"></a>
<FONT color="green">168</FONT>             * @param constant A constant Complex number to multiply a matrix<a name="line.168"></a>
<FONT color="green">169</FONT>             * @return Matrix c<a name="line.169"></a>
<FONT color="green">170</FONT>             */<a name="line.170"></a>
<FONT color="green">171</FONT>            public Matrix multiplyMatrix(Complex constant){<a name="line.171"></a>
<FONT color="green">172</FONT>                    Matrix c = new  Matrix(this.getWidth(),this.getHeight());<a name="line.172"></a>
<FONT color="green">173</FONT>    <a name="line.173"></a>
<FONT color="green">174</FONT>                    for ( int i=0; i &lt; c.getHeight(); i++){<a name="line.174"></a>
<FONT color="green">175</FONT>                            for ( int j = 0; j &lt; c.getWidth(); j++){<a name="line.175"></a>
<FONT color="green">176</FONT>                                    c.setElement(j, i,Complex.multiplyComplex(constant,this.getElement(j, i)));<a name="line.176"></a>
<FONT color="green">177</FONT>                            }<a name="line.177"></a>
<FONT color="green">178</FONT>                    }<a name="line.178"></a>
<FONT color="green">179</FONT>                    return c;<a name="line.179"></a>
<FONT color="green">180</FONT>            }<a name="line.180"></a>
<FONT color="green">181</FONT>    <a name="line.181"></a>
<FONT color="green">182</FONT>            /**<a name="line.182"></a>
<FONT color="green">183</FONT>             *  Method to multiply a matrix by itself power number of times.<a name="line.183"></a>
<FONT color="green">184</FONT>             * @param pow The Number of times to multiply the matrix by itself.<a name="line.184"></a>
<FONT color="green">185</FONT>             * @return Matrix c Answer.<a name="line.185"></a>
<FONT color="green">186</FONT>             */<a name="line.186"></a>
<FONT color="green">187</FONT>            public Matrix powerMatrix(int pow){<a name="line.187"></a>
<FONT color="green">188</FONT>                    if(pow&lt;1){<a name="line.188"></a>
<FONT color="green">189</FONT>                            throw new IllegalArgumentException("ERROR: Power Must be greater than 0.");<a name="line.189"></a>
<FONT color="green">190</FONT>                    }<a name="line.190"></a>
<FONT color="green">191</FONT>    <a name="line.191"></a>
<FONT color="green">192</FONT>                    Matrix c = new Matrix(this.getWidth(),this.getHeight());<a name="line.192"></a>
<FONT color="green">193</FONT>    <a name="line.193"></a>
<FONT color="green">194</FONT>                    c=this;<a name="line.194"></a>
<FONT color="green">195</FONT>                    for ( int i=1; i&lt;pow;i++){<a name="line.195"></a>
<FONT color="green">196</FONT>                            c = c.multiplyMatrix(this);<a name="line.196"></a>
<FONT color="green">197</FONT>                    }<a name="line.197"></a>
<FONT color="green">198</FONT>                    return c;<a name="line.198"></a>
<FONT color="green">199</FONT>            }<a name="line.199"></a>
<FONT color="green">200</FONT>    <a name="line.200"></a>
<FONT color="green">201</FONT>            /**<a name="line.201"></a>
<FONT color="green">202</FONT>             * Add a matrix to this matrix. Matrices must have same dimension<a name="line.202"></a>
<FONT color="green">203</FONT>             * @param b Matrix to add to this<a name="line.203"></a>
<FONT color="green">204</FONT>             * @return c Matrix this + b<a name="line.204"></a>
<FONT color="green">205</FONT>             * @throws Illegal argument exception<a name="line.205"></a>
<FONT color="green">206</FONT>             */<a name="line.206"></a>
<FONT color="green">207</FONT>            public Matrix addMatrix(Matrix b){<a name="line.207"></a>
<FONT color="green">208</FONT>                    // Deal with exception<a name="line.208"></a>
<FONT color="green">209</FONT>                    if ( this.getWidth()!= b.getWidth() || this.getHeight() != b.getHeight()){<a name="line.209"></a>
<FONT color="green">210</FONT>                            throw new MatrixSizeException("Dimensions of the two matrices must be the same.\n" +<a name="line.210"></a>
<FONT color="green">211</FONT>                                            "this: " + this.getWidth() + "x" + this.getHeight() + "\n" +<a name="line.211"></a>
<FONT color="green">212</FONT>                                            "b: " + b.getWidth() + "x" + b.getHeight());<a name="line.212"></a>
<FONT color="green">213</FONT>                    }<a name="line.213"></a>
<FONT color="green">214</FONT>                    // Simple matrix addition<a name="line.214"></a>
<FONT color="green">215</FONT>                    Matrix c = new Matrix(this.getWidth(),this.getHeight());<a name="line.215"></a>
<FONT color="green">216</FONT>                    for ( int i = 0; i &lt; this.getWidth(); i++){<a name="line.216"></a>
<FONT color="green">217</FONT>                            for ( int j = 0; j &lt; this.getHeight(); j++){<a name="line.217"></a>
<FONT color="green">218</FONT>                                    c.setElement(i, j,Complex.addComplex(this.getElement(i, j), b.getElement(i, j)));<a name="line.218"></a>
<FONT color="green">219</FONT>                            }<a name="line.219"></a>
<FONT color="green">220</FONT>                    }<a name="line.220"></a>
<FONT color="green">221</FONT>                    return c;<a name="line.221"></a>
<FONT color="green">222</FONT>            }<a name="line.222"></a>
<FONT color="green">223</FONT>    <a name="line.223"></a>
<FONT color="green">224</FONT>            /**<a name="line.224"></a>
<FONT color="green">225</FONT>             * Method returns the transpose of this matrix<a name="line.225"></a>
<FONT color="green">226</FONT>             * @return Matrix transpose of this<a name="line.226"></a>
<FONT color="green">227</FONT>             */<a name="line.227"></a>
<FONT color="green">228</FONT>            public Matrix transposeMatrix(){<a name="line.228"></a>
<FONT color="green">229</FONT>                    Matrix m = new Matrix(this.getHeight(),this.getWidth());<a name="line.229"></a>
<FONT color="green">230</FONT>                    for (int i = 0; i &lt; this.getHeight(); i++){<a name="line.230"></a>
<FONT color="green">231</FONT>                            for ( int j = 0; j &lt; this.getWidth(); j++){<a name="line.231"></a>
<FONT color="green">232</FONT>                                    m.setElement(i, j, this.getElement(j, i));<a name="line.232"></a>
<FONT color="green">233</FONT>                            }<a name="line.233"></a>
<FONT color="green">234</FONT>                    }<a name="line.234"></a>
<FONT color="green">235</FONT>                    return m;<a name="line.235"></a>
<FONT color="green">236</FONT>            }<a name="line.236"></a>
<FONT color="green">237</FONT>    <a name="line.237"></a>
<FONT color="green">238</FONT>            /**<a name="line.238"></a>
<FONT color="green">239</FONT>             * Return a matrix as a string for printing to the terminal.<a name="line.239"></a>
<FONT color="green">240</FONT>             * Output will span as many lines as there are rows<a name="line.240"></a>
<FONT color="green">241</FONT>             * @return String of a matrix<a name="line.241"></a>
<FONT color="green">242</FONT>             */<a name="line.242"></a>
<FONT color="green">243</FONT>            public String toString(){<a name="line.243"></a>
<FONT color="green">244</FONT>                    String out = "";<a name="line.244"></a>
<FONT color="green">245</FONT>                    for (int i = 0; i &lt; this.getHeight(); i++){<a name="line.245"></a>
<FONT color="green">246</FONT>                            out+="|";<a name="line.246"></a>
<FONT color="green">247</FONT>                            for (int j = 0; j &lt; this.getWidth(); j++){<a name="line.247"></a>
<FONT color="green">248</FONT>                                    out+= " "+this.getElement(j, i).toString();<a name="line.248"></a>
<FONT color="green">249</FONT>                            }<a name="line.249"></a>
<FONT color="green">250</FONT>                            out+=" |\n";<a name="line.250"></a>
<FONT color="green">251</FONT>                    }<a name="line.251"></a>
<FONT color="green">252</FONT>                    return out;<a name="line.252"></a>
<FONT color="green">253</FONT>            }<a name="line.253"></a>
<FONT color="green">254</FONT>    <a name="line.254"></a>
<FONT color="green">255</FONT>            /**<a name="line.255"></a>
<FONT color="green">256</FONT>             * <a name="line.256"></a>
<FONT color="green">257</FONT>             * Create an identity matrix. <a name="line.257"></a>
<FONT color="green">258</FONT>             * Matrix will be size x size square matrix.<a name="line.258"></a>
<FONT color="green">259</FONT>             * @param size Size of the matrix<a name="line.259"></a>
<FONT color="green">260</FONT>             * @return Identity matrix<a name="line.260"></a>
<FONT color="green">261</FONT>             */<a name="line.261"></a>
<FONT color="green">262</FONT>            public static Matrix IdentityMatrix(int size){<a name="line.262"></a>
<FONT color="green">263</FONT>                    Matrix identity = new Matrix(size,size,0);<a name="line.263"></a>
<FONT color="green">264</FONT>                    for (int i=0; i&lt;size; i++){<a name="line.264"></a>
<FONT color="green">265</FONT>                            identity.setElement(i, i, new Complex(1,0));<a name="line.265"></a>
<FONT color="green">266</FONT>                    }<a name="line.266"></a>
<FONT color="green">267</FONT>                    return identity;<a name="line.267"></a>
<FONT color="green">268</FONT>            }<a name="line.268"></a>
<FONT color="green">269</FONT>    }<a name="line.269"></a>




























































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